Question

Find the slope of the tangent line to f(x)=e4x2+5x at the point where x=0

Answer 1

We find the first derivative of the curve, and evaluate it at x=1 (which we will use to obtain the slope of the line tangent to the curve at (1,−1)). So we have a point on the tangent line: (x0,y0)=(1,−1) and the slope of the line tangent at that point: m=−13.